# Maximum subarray sum in O(n) using prefix sum in C++

## Problem statement

Given an Array of Positive and Negative Integers, find out the Maximum Subarray Sum in that Array

## Example

If input array is − {-12, -5, 4, -1, -7, 1, 8, -3} then output is 9

## Algorithm

• Calculate the prefix sum of the input array.

• Initialize− min_prefix_sum = 0, res = -infinite

• Maintain a loop for i = 0 to n. (n is the size of the input array).

• cand = prefix_sum[i] – mini

• If cand is greater than res (maximum subarray sum so far), then update res by cand.

• If prefix_sum[i] is less than min_prefix_sum (minimum prefix sum so far), then update min_prefix_sum by prefix_sum[i].

• Return res

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
int maximumSumSubarray(int *arr, int n){
int minPrefixSum = 0;
int res = numeric_limits<int>::min();
int prefixSum[n];
prefixSum[0] = arr[0];
for (int i = 1; i < n; i++) {
prefixSum[i] = prefixSum[i - 1] + arr[i];
}
for (int i = 0; i < n; i++) {
res = max(res, prefixSum[i] - minPrefixSum);
minPrefixSum = min(minPrefixSum, prefixSum[i]);
}
return res;
}
int main(){
int arr[] = {-12, -5, 4, -1, -7, 1, 8, -3};
int n = sizeof(arr) / sizeof(arr[0]);
cout << "Result = " << maximumSumSubarray(arr, n) <<endl;
return 0;
}

## Output

When you compile and execute above program. It generates following output −

Result = 9

Updated on: 30-Jan-2020

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